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Each day at Dans new job, he earns $10 more than the day before. If h 09 Apr 2020, 03:42
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A
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58% (01:51) correct 42% (01:33) wrong based on 457 sessions

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Each day at Dan’s new job, he earns $10 more than the day before. If he just completed his 15th day of work, how much did he earn on his first day?

(1) His total earnings for the three most recent work days equal $690.

(2) His total earnings for the three most recent work days exceed his total earnings for the first three work days by $360


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Each day at Dans new job, he earns $10 more than the day before. If h 09 Apr 2020, 07:21
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Bunuel
Each day at Dan’s new job, he earns $10 more than the day before. If he just completed his 15th day of work, how much did he earn on his first day?

(1) His total earnings for the three most recent work days equal $690.

(2) His total earnings for the three most recent work days exceed his total earnings for the first three work days by $360


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Solution


Step 1: Analyse Question Stem


    • Let x be the earning on day 1.
    o Earning on nth day = \(x + (n-1)*10\)
We need to find the value of x.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: His total earning for the three most recent work days equal $690
    • Three most recent days are 15th, 14th, and 13th day
      o Earning on recent three days = \(x + (13-1)*10 +x + (14-1)*10 + x+(15-1)*10\)
      o \(690 = x + 120 + x + 130 +x +140\)
      o \(690 = 3x + 390\)
         This is a linear equation with one variable.
    • We can find the value of x.
Hence, statement 1 is sufficient, we can eliminate the answer options B, C and E.
Statement 2: His total earning for the recent three days exceeds his total earning for the first three days by $ 360
    • Earning on first 3 days = \(x + x+10 +x +20= 3x + 30\)
    • Earning on last three days = \(x + 120 + x +130 +x +140 = 3x + 390\)
      o According to given information,
      o \(3x + 390 -3x -30 = 360\)
      o \(360 = 360\)
         We cannot find the value of x.
Hence, statement 2 is not sufficient, the correct answer is Option A.­
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Each day at Dans new job, he earns $10 more than the day before. If h Updated on: 29 Apr 2024, 01:07
Originally posted by Archit3110 on 09 Apr 2020, 04:35.
Last edited by Bunuel on 29 Apr 2024, 01:07, edited 2 times in total.
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target to determine is earning value of day 1
each day Dan earns $10 more than other day
so day 1 = x
day 2 = x+10
day 3 = x+30
so on till day 15 ; x+140
#1
His total earnings for the three most recent work days equal $690.
recent three days ; day 13,14,15 ; and day 14 value would be mean of 690 ; 690/3 ; $330
so day x+130=330
x= $200
sufficient
#2
His total earnings for the three most recent work days exceed his total earnings for the first three work days by $360
three most recent days salary
3x+ ( 120+130+140) ; 3x+ 390
and salary of first 3 days ; 3x+(10+20) ; 3x+30
we are given
3x+390=3x+30+360
value of x cannot be determined
insufficient
IMO A

Bunuel
Each day at Dan’s new job, he earns $10 more than the day before. If he just completed his 15th day of work, how much did he earn on his first day?

(1) His total earnings for the three most recent work days equal $690.

(2) His total earnings for the three most recent work days exceed his total earnings for the first three work days by $360


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Each day at Dans new job, he earns $10 more than the day before. If h 09 Apr 2020, 08:08
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Hi,Archit3110

I guess there are couple of mistakes (Not in the final answer though ;) ),i have marked the errors in red in your quoted answer.
Day 3= x+20
and
690/3=230 and not 330.
Hence x=100.
However as far as it is DS,none of it would matter :D
Please correct me if i am wrong.


Archit3110
target to determine is earning value of day 1
each day Dan earns $10 more than other day
so day 1 = x
day 2 = x+10
day 3 = x+30
so on till day 15 ; x+140
#1
His total earnings for the three most recent work days equal $690.
recent three days ; day 13,14,15 ; and day 14 value would be mean of 690 ; 690/3 ; $330
so day x+130=330
x= $200
sufficient
#2
His total earnings for the three most recent work days exceed his total earnings for the first three work days by $360
three most recent days salary
3x+ ( 120+130+140) ; 3x+ 390
and salary of first 3 days ; 3x+(10+20) ; 3x+30
we are given
3x+390=3x+30+360
value of x cannot be determined
insufficient
IMO A


Bunuel
Each day at Dan’s new job, he earns $10 more than the day before. If he just completed his 15th day of work, how much did he earn on his first day?

(1) His total earnings for the three most recent work days equal $690.

(2) His total earnings for the three most recent work days exceed his total earnings for the first three work days by $360


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Each day at Dans new job, he earns $10 more than the day before. If h 09 Apr 2020, 11:14
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[quote="Bunuel"]Each day at Dan’s new job, he earns $10 more than the day before. If he just completed his 15th day of work, how much did he earn on his first day?

(1) His total earnings for the three most recent work days equal $690.

(2) His total earnings for the three most recent work days exceed his total earnings for the first three work days by $360
The pattern of earnings : a, a+ 10, a+20, a+30....So on the 15th day the earnings will be a +140.
1) 3a+ (140+130+120) = 690. Sufficient
2) (3a + 390) -( 3a +30) = 360. a rules out. Not Sufficient.
A is the answer.
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Each day at Dans new job, he earns $10 more than the day before. If h 26 Jun 2021, 09:24
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Note that the daily increase is consistent: he always earns $10 more each day. This is essentially a consecutive integer problem (although, in this case, there are increments of 10, not 1). Use f to represent Dan’s earnings on the first day. Express his earnings on subsequent days as f + 10, f + 20, f + 30, … f + 140.

(1) SUFFICIENT: This statement provides the sum of the most recent three days:

(f + 120) + (f + 130) + (f + 140) = $690
3f + 390 = $690
3f = $300
f = $100

Dan earned $100 on his first day.

(2) INSUFFICIENT: This statement provides the difference between the totals for the first three days and the last three days:

First three days = (f) + (f + 10) + (f + 20) = 3f + 30
Last three days = (f + 120) + (f + 130) + (f + 140) = 3f + 390
Last three days − First three days = (3f + 390) − (3f + 30) = $360

This statement is always true, regardless of how much Dan made on the first day. (This information can be determined from the question stem alone!)
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Each day at Dans new job, he earns $10 more than the day before. If h 08 Mar 2025, 13:36
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